document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=538428>Question 538428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular sheet of perimeter 40 cm and dimensions x cm by y cm is to be rolled into a cylinder.  What values of x and y given the largest cylinder volume? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353174 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=353174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular sheet of perimeter 40 cm and dimensions x cm by y cm is to be rolled into a cylinder.  What values of x and y given the largest cylinder volume?<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "2(x + y) = 40<BR>\n" );
document.write( "y = 20 - x<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "x = 2*pi*r<BR>\n" );
document.write( "r = x/2pi<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Vol = pi*r^2*y = pi*(x/2pi)^2*(20 - x)<BR>\n" );
document.write( "Vol = x^2*(20-x)/4pi<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Vol+=+%2820x%5E2+-+x%5E3%29%2F4pi ALIGN=MIDDLE  ALT=\"Vol+=+%2820x%5E2+-+x%5E3%29%2F4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dV/dx = (1/4pi)*(40x - 3x^2) = 0<BR>\n" );
document.write( "3x^2 = 40x<BR>\n" );
document.write( "x = 40/3<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Local max at x = 40/3, y = 20/3 cm<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "PS  Max volume = 94.314 cc\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );